Geodesic
Poincaré Lemma on Quaternion-like Heisenberg Groups
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 495-508

Voir la notice de l'article provenant de la source Cambridge University Press

For smooth functions ${{a}_{1}}\,,\,{{a}_{2}}\,,\,{{a}_{3}}\,,\,{{a}_{4}}\,$ on a quaternion Heisenberg group, we characterize the existence of solutions of the partial differential operator system ${{X}_{1}}f\,=\,{{a}_{1}},\,{{X}_{2}}f=\,{{a}_{2}},\,{{X}_{3}}f\,=\,{{a}_{3}},\,\text{and}\,{{X}_{4}}f\,=\,{{a}_{4}}$ . In addition, a formula for the solution function $f$ is deduced, assuming solvability of the system.
DOI : 10.4153/CMB-2017-027-4
Mots-clés : 93B05, 49N99, bracket generating property, quaternion Heisenberg group, curl, integrability condition, Poincaré lemma 
Chang, Der-Chen; Yang, Nanping; Wu, Hsi-Chun. Poincaré Lemma on Quaternion-like Heisenberg Groups. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 495-508. doi: 10.4153/CMB-2017-027-4
@article{10_4153_CMB_2017_027_4,
     author = {Chang, Der-Chen and Yang, Nanping and Wu, Hsi-Chun},
     title = {Poincar\'e {Lemma} on {Quaternion-like} {Heisenberg} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {495--508},
     year = {2018},
     volume = {61},
     number = {3},
     doi = {10.4153/CMB-2017-027-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/}
}
TY  - JOUR
AU  - Chang, Der-Chen
AU  - Yang, Nanping
AU  - Wu, Hsi-Chun
TI  - Poincaré Lemma on Quaternion-like Heisenberg Groups
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 495
EP  - 508
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/
DO  - 10.4153/CMB-2017-027-4
ID  - 10_4153_CMB_2017_027_4
ER  - 
%0 Journal Article
%A Chang, Der-Chen
%A Yang, Nanping
%A Wu, Hsi-Chun
%T Poincaré Lemma on Quaternion-like Heisenberg Groups
%J Canadian mathematical bulletin
%D 2018
%P 495-508
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/
%R 10.4153/CMB-2017-027-4
%F 10_4153_CMB_2017_027_4

[1] [1] Calin, O., Chang, D. C., and Eastwood, M., Integrability conditions for Heisenberg and Grushin-type distributions. Anal. Math. Phys. 4(2014), no. 1-2, 99–114. http://dx.doi.Org/10.1007/s13324-014-0073-1 Google Scholar

[2] [2] Calin, O., Chang, D. C., and Hu, J., Poincare's lemma on the Heisenberg group. Adv. in Appl. Math. 60(2014), 90–102. http://dx.doi.org/10.101 6/j.aam.2014.08.003 Google Scholar

[3] [3] Chang, D. C., Markina, I., and Wang, W., On the Cauchy-Szegö kernet for quaternion Siegel upper half-space. Complex Anal. Oper. Theory 7(2013), no. 5, 1623–1654. http://dx.doi.Org/10.1007/s11785-012-0282-2 Google Scholar

[4] [4] Chow, W.-L., Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann. 117(1939), 98–105. http://dx.doi.Org/10.1007/BF01450011 Google Scholar

[5] [5] Fefferman, C. and Phong, D. H., The uncertainty principle and sharp Garding inequalities. Comm. Pure and Applied Math. 34(1981), 285–331. http://dx.doi.org/10.1002/cpa.3160340302 Google Scholar

[6] [6] Hörmander, L., Hypoelliptic second order differential equations. Acta Math. 119(1967), 147–171. http://dx.doi.org/10.1007/BF02392081 Google Scholar

[7] [7] Wang, W., The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group. J. Geom. Phys. 61(2011), 363–380. http://dx.doi.Org/10.1016/j.geomphys.2010.10.006 Google Scholar

Cité par Sources :